Minimal Polynomials of Some Eta-Quotients Evaluated at CM Points

Ho Yun Jung ()
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Ho Yun Jung: Department of Mathematics, Dankook University, Cheonan-si 31116, Republic of Korea

Mathematics, 2025, vol. 13, issue 19, 1-13

Abstract: We study certain eta-quotients of weight zero evaluated at CM points of imaginary quadratic orders. Using the theory of extended form class groups, we show that these special values generate the corresponding ring class fields and we provide explicit descriptions of their minimal polynomials. Finally, we apply these results to certain Diophantine problems.

Keywords: class field theory; form class groups; ideal class groups; modular functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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